The sum of a harmonic series is never an integer unless ___ and ___ are both equal to 1.

The first term a = 1 and the number of terms n = 1

True or False: The harmonic mean is always greater than or equal to the geometric mean.

False; the harmonic mean is always less than or equal to the geometric mean.

In a harmonic progression, if the three numbers are a, b, and c, then the relationship between them can be expressed as ___.

2/b = 1/a + 1/c

What is the 8th term of the harmonic series derived from 1/2, 1/4, 1/6?

1/16

Fill in the blank: The harmonic mean of two numbers a and b is calculated as ___ when both are not equal to zero.

2ab / (a + b)

The relationship A ≥ G ≥ H is true for which means where A is the arithmetic mean, G is the geometric mean, and H is the harmonic mean? Provide the condition where this holds.

This holds for any two positive numbers.

If the harmonic mean of two numbers is 8 and one of the numbers is 12, the other number is ___.

6

True or False: The inverse of a harmonic progression results in an arithmetic progression.

True

Find the middle term in the harmonic series 4, a, 6. If a equals ___, calculate the value.

22/5

What type of series is represented when converting a harmonic series into an arithmetic series?

An arithmetic progression.

For the numbers 4 and 6, what is the geometric mean?

4.89

Fill in the blank: The nth term of a harmonic series can be derived by converting the series to ___ form.

Arithmetic progression